A rotation can be represented, e.g., as Euler angles, a rotation matrix, a quaternion, or with the axis-angle representation.
Euler angles are known to suffer from gimbal lock discontinuity [1]}.
Rotation matrices and quaternions have orthogonality and unit norm constraints, respectively.
Such constraints may be problematic in an optimization-based approach such as supervised learning, since they restrict the range of valid predictions.
To avoid these issues, we adopt the axis-angle representation.
In the axis-angle representation, a vector \(\mathbf {r}\in \mathbb {R}^3\)  represents a rotation of \(\theta = \left\Vert \mathbf {r} \right\Vert _2\)  radians around the unit vector \(\frac{\mathbf {r}}{\left\Vert \mathbf {r} \right\Vert _2}\)  [2]}.
